There are many examples of clamps or chucks used to hold successive workpieces in position for various processing steps. Commonly, such jaws use springs and/or bolts to maintain tension. However, these require time and effort for each manual release and resetting when changing a workpiece. Also, when the fastened workpiece is necessarily subject to operational vibration, this tends to loosen or weaken the permanence of the clamping force, whether produced by springs or screw threads. Accordingly, it would be desirable to have such jaws operative with more certain or constant clamping means which at the same time could be instantly set and realeased as desired. While various vacuum chucks are old, particularly those with pairs of oppositely curved jaws applicable to tubular workpieces, these do not provide the present leveraged clamping applied to a straight edge by a non-hinged, self-aligning tiltable plate jaw and also such past constructions are not adapted to be correlated with the composite operation of an opthalmic polishing or grinding machine. However, use of the present fluid-operated chuck is not limited to association with this particular type of assembly or operation.